Robust closed-loop control of plasma glycemia: A discrete-delay model approach

Abstract

Abstract. The paper investigates the problem of tracking a desired plasma glucose evolution by means of intra-venous insulin administration. A modelbased approach is followed. A recent model of the glucose/insulin regulatory system which consists of discrete-delay nonlinear differential equations is used. A disturbance is added to the insulin kinetics in order to model uncertainties concerning both the insulin delivery rate and the mechanism actuating the insulin pump. A feedback control law which yields input-to-state stability of the closed loop error system with respect to the disturbance is provided. Such control law depends on the glucose and insulin measurements at the present and at a delayed time. In silico simulations validate the theoretical results.

A therapy parameter-based model for predicting blood glucose concentrations in patients with type 1 diabetes

“…This would associate a confidence interval to any prediction, which is of high value. These results could be applied in the context of robust control such as proposed by, e.g., Kovács et al, Chee et al, or Palumbo et al [37][38][39].…”

Local sampled-data control of the glucose-insulin system

“…The state feedback k in forthcoming Theorem 2 has been designed in a continuous time basis in [28], by means of the change of variables in (10).…”

“…We considered, for simulation, the case 3 (severe hyperglycemia, establishment of a state of frank Type 2 Diabetes Mellitus) reported in [28] (see Table I, where G b and I b denote steady state values of glycemia and insulinemia when no control action is taken, i.e., when v(t) ≡ 0, t ∈ R + ). As far as the eigenvalues for the matrix H in (14) are concerned, they are chosen equal to −0.02, −0.03.…”

“…A state feedback (continuous or not) is said to be a local stabilizer in the sample-and-hold sense if, for a suitable initial ball and an arbitrary small ball of the origin, there exists a suitable small sampling period such that the feedback control law obtained by sampling and holding the above state feedback, with the given sampling period, keeps uniformly bounded all the trajectories starting in any point of the initial ball and, moreover, drives all such trajectories into the small ball, uniformly in a maximum finite time, keeping them in, thereafter. Here, it is proved theoretically that the implementation by sampling and holding, for suitable small sampling period, of a given state feedback designed in the continuous time basis, which is shown in the literature to yield local stabilization (see [28]), provides local stabilization in the sample-and-hold sense. This result is expected, nevertheless its non trivial theoretical proof allows us to add a further important property to this controller proposed in the literature by the authors, which has been shown to perform very well when checked in closed-loop on a population of virtual patients modeled by means of the computer simulator in [17], accepted by the Food and Drug Administration (FDA) as a substitute to animal trials for the preclinical testing of control strategies in artificial pancreas (see [30]).…”

Closed-loop control scheme for the Euglycemic Hyperinsulinemic Clamp: validation on virtual patients

“…Denote G(t), [mM], I(t), [pM], plasma glycemia and insulinemia, respectively. The glucose-insulin model considered for the EHC is a slight modification of the DDE one in exploited with the purpose of glucose control in Type 2 diabetic patients (see Palumbo et al, 2009, Palumbo et al, 2011, Palumbo et al, 2012 for the details on the model parameters):…”